How do you expand #(2x+5)^7#?
2 Answers
Explanation:
So
This works regardless of whats in the brackets.
And without brackets
And so forth.
Explanation:
#"using the "color(blue)"binomial theorem"#
#• (x+y)^n=sum_(r=0)^n((n),(r))x^(n-r)y^r#
#"where " ((n),(r))=(n!)/(r!(n-r)!)#
#"here " x=2x" and " y=5#
#rArr(2x+5)^7#
#=((7),(0))(2x)^7 .5^0+((7),(1))(2x)^6 .5^1+((7),(2))(2x)^5 .5^2#
#color(white)(=)+((7),(3))(2x)^4 .5^3+((7),(4))(2x)^3 .5^4+((7),(5))(2x)^2 .5^5#
#color(white)(=)+((7),(6))(2x)^1 .5^6+((7),(7))(2x)^0 .5^7#
#"we can obtain the binomial coefficients using the "#
#"appropriate row of "color(blue)"Pascal's triangle"#
#"for n = 7 the row of coefficients is"#
#1color(white)(x)7color(white)(x)21color(white)(x)35color(white)(x)35color(white)(x)21color(white)(x)7color(white)(x)1#
#=1. 128x^7+7.5.64x^6+21.25.32x^5+35.125.16x^4#
#color(white)(=)+35.625.8x^3+21.3125.4x^2+7.15625.2x+78125#
#=128x^7+2240x^6+16800x^5+70000x^4+175000x^3#
#color(white)(=)+262500x^2+218750x+78125#